0.4 Gram equivalent concept

Mole concept is based on molecular weight. An equivalent concept is “gram equivalent weight” or “gram equivalent” concept. It is based on equivalent weight. Equivalent weight is measure of mass proportion of an element, compound or ion in which it combines with the mass of other chemical entities. Mass of one gram equivalent, like its mole counterpart, is equal to mass in gram, which is numerically equal to equivalent weight.

Equivalent weight (e)

Equivalent weight unlike molecular weight is proportional mass of chemical entities which combine or displace other chemical entities.

Equivalent weight

It is defined as the mass of an element/compound/ion which combines or displaces 1 part of hydrogen or 8 parts of oxygen or 35.5 parts of chlorine by mass.

It is not always possible to apply this classic definition to determine equivalent weights of chemical entities. It is so because, we can not conceive of reactions involving chemical entities with three named reference of hydrogen, oxygen and chlorine. Generally, we are limited to determination of equivalent weights of elements and few compounds by using this definition of equivalent weight. A more workable definition is given as :

$$\text{Equivalent weight},E=\frac{\text{Molecular weight}}{\text{Valence factor}}=\frac{M_O}{x}$$

Clearly, determination of equivalent weight amounts to determining valence factor “x”. Here, we shall classify chemical entities and the techniques to determine “x”.

Equivalent weight of an element

In the case of an element, the equivalent weight is defined as :

$$\text{Equivalent weight},E=\frac{\text{Atomic weight}}{\text{Valency}}=\frac{A}{x}$$

Note that atomic weight substitutes molecular weight and valency substitutes valence factor in the definition. Valencies of hydrogen, calcium and oxygen are 1,2 and 2 respectively. Hence, their equivalent weights are 1/1 =1, 40/2 = 20 and 16/2 = 8 respectively.

Equivalent weight of an acid

The valence factor of an acid is equal to its basicity. The basicity of an acid is equal to furnishable hydrogen ion (proton) in its aqueous solution. Importantly, basicity is not same as the number of hydrogen atoms in acid molecule. Consider acetic acid (CH3COOH). It contains 4 hydrogen atoms in it, but only 1 furnishable hydrogen ion. As such, basicity of acetic acid is 1. With this background, we define equivalent weight of an acid as :

$$\text{Equivalent weight},E=\frac{\text{Molecular weight of acid}}{\text{Basicity}}$$

Basicity of sulphuric acid is 2. Hence, equivalent weight of sulphuric acid ( $H_{2}S{O}_4$ ) is (2X1 + 32 + 4X16)/2 = 98/2 = 49. Similarly, basicity of oxalic acid is 2. Hence, equivalent weight of oxalic acid ( $H_2{C}_2{O}_4$ ) is (2X1 + 2X12 + 4X16)/2 = 90/2=45.

Phosphorous based acids like phosphoric acid ( $H_{3}P{O}_4$ ), phosphorous acid ( $H_{3}P{O}_3$ ) and hypo-phosphorous acid ( $H_{3}P{O}_2$ ) need special mention here to understand their basicity. The structures of three acids are shown here. From the structure, it appears that these compounds may furnish OH ions, but bond strengths between phosphorous and oxygen (P-O) and phosphorous and hydrogen (P-H) are stronger than between oxygen and hydrogen (O-H) in –OH group. As such, these molecules release hydrogen ions from –OH group and behave as acid. Clearly, basicities of phosphoric acid ( $H_{3}P{O}_4$ ), phosphorous acid ( $H_{3}P{O}_3$ ) and hypo-phosphorous acid ( $H_{3}P{O}_2$ ) are 3, 2 and 1 respectively.